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Construction by the Tikhonov Method of a Nonzero Solution of the Homogeneous Cauchy Problem for one Equation with a Fractional Derivative |
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PP: 23-27 |
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doi:10.18576/pfda/100103
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Author(s) |
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Bakhrom Irgashev,
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Abstract |
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| In this article, for a homogeneous equation of high even order with a fractional derivative in the sense of Caputo, a non- trivial solution of the homogeneous Cauchy problem in the upper half-plane is constructed by the method of A.N.Tikhonov. The idea of the method is that the solution is constructed as a series of infinitely differentiable functions with certain estimates. The values of the functions themselves and derivatives of any order at the initial point are equal to 0. The existence of such functions follows from the works of Carleman on quasi-analytic functions.
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